Classical mechanics, of course, is a full discipline by itself. It can be learned and developed without reference to any other physical theory. Dynamical systems, orbital dynamics, chaos, and fractal dynamics are examples of modern developments. On the other hand, we live in a world that has molecular and atomic physics, quantum mechanics, quantum field theory, general and special relativity, quantum information. Our fundamental understanding of nature is coded in the standard model of elementary particles, and the theory of the Big Bang. It is not only a waste to study classical mechanics as a separate subject, but it is imperative to understand how all other physical theories rely on classical mechanics in fundamentals and techniques.
Here we explore two main ideas. The first one is that physics is the science that maps natural phenomena into mathematical structures. The other idea is that a physical system is only as definable as it can be measured, and the information that defines a system is the one all observers in a specified class of observers agree.